This is the error I received when I tried to insert my newly created SharePoint App in a web page.

The solution was to include the following tag into the aspx page which was mapped with the Client Web Part.

<WebPartPages:AllowFraming runat="server"/>

This is done because, SharePoint adds X-FRAME-OPTIONS: SAMEORIGIN in the HTTP response header which, in a page, will allow framing from the current domain only, blocking all the other external sites. More details can be found here.

To overcome this, we need to explicitly enable the AllowFraming option in the corresponding pages as, by its very design, App code does not reside on the same server as SharePoint.